Bad news for my brother's marathon aspirations. I just redid my own marathon calculations, using my latest numbers. Ran 6mi at an 8:06 pace yesterday, and 3mi at a 7:55 pace today. Came up with the following:

Let pace = v
Let distance = x
Assume v is a function of x (as opposed to a function of time).

Assume (∆v/∆x) is linear. Because I don’t feel like doing calculus.

v_3mi = 7:55 = 475 sec/mi
v_6mi = 8:06 = 486 sec/mi

∆x = (6mi – 3mi) = 3mi
∆v = (486 sec/mi – 475 sec/mi) = 11 sec/mi

So it’s pretty easy to figure (∆v/∆x) = 11/3 sec/mi²

Assuming a straight linear function (y = mx + b), 11/3 will obviously be the slope of the line (m).

So y = 11/3x + b

Substituting to solve for b:

475 = (11/3)(3) + b (alternately, 486 = (11/3)(6) + b)

Therefore b = 464 (yes, for either substitution; that’s why we call it “linear.”)

So for a marathon, (x = 26.2 mi), solve for y (v_26.2mi):

v_26.2mi = (11/3)(26.2) + 464 = 8401/15 sec/mi

Which works out to a 9:20 pace over the course of the run.

Which means a time of 4hrs 4min 32sec for the marathon. Not quite as impressive.

The only problem with using a linear function is that the fastest I could ever run would be a 464sec/mi pace, which is like a 7:44. Which means that it'd take me over 26 seconds to run 10 yards.

Remind me again why I don't have a hot Italian girlfriend?